Constant Material Properties Research Articles

Effect of free vibration on mechanical characteristics of Bi-directional functionally graded beams under hygrothermal effect

ABSTRACT The effect of free vibration on mechanical characteristics of bi-directional functionally graded material (BDFGM) beams under the influence of hygrothermal effects involves the application of the harmonic differential quadrature method (HDQM). The material parameters are supposed to vary in both axial and thickness directions. The temperature distribution is employed along the length direction of the BDFGM beams while maintaining a constant moisture concentration. An exponential law with axial thermal variation under moisture effect is investigated to analyse vibration behaviour in the BDFGM beams using the HDQM. Hamilton’s principle is used to obtain governing equations. Three kinds of temperature distribution profile were considered i.e. uniform (UTR), linear (LTR) and nonlinear temperature rise (NLTR). Free vibration analysis is performed using the HDQM. The precision of the HDQM is validated by comparing it with prior studies. Various configurations of boundary conditions, including supported, clamped, and free, are considered. Parametric results are investigated to explore the effect of the exponent parameters, temperature profile and constant humidity content. Results indicate that temperature, constant moisture content, material properties, and different end conditions significantly influence natural frequency. The outcomes can be applied to designing two or more directional FGM structures for different environmental conditions.

A combined uncertainty and sensitivity analysis of melting in a cubical cavity, Part A: Model validation

Latent heat thermal energy storage systems exploit the solid–liquid phase transition of a material to store thermal energy almost isothermally with high energy density. Numerical methods are increasingly being used for the targeted design of these storage systems. The problem, however, is that the results obtained with these methods – despite a frequently shown near-perfect agreement between validation experiments and simulation results – are subject to large uncertainty. To illustrate the extent of this problem and to show approaches to solving it, a combined uncertainty and sensitivity analysis of the melting process of a paraffin (octadecane) in a cuboid heated from one side is carried out in this two-paper series. In part A, we present the model and validate it; in part B we use it to carry out the combined uncertainty and sensitivity analysis. The validation of the model is performed with the help of experimental results. For this purpose, we measure the liquid phase fraction, the position of the phase boundary, the velocity field in the liquid and the temperature inside the test capsule. We make sure that the experimental results are reproducible. Systematic deviations are discussed and, if possible, the results are corrected for their value. When measuring the velocity field using particle image velocimetry (PIV), the greatest systematic deviation is due to the inhomogeneous refractive index field in the liquid phase. Finally, it is shown that, in the present case, the influence is very low if constant material properties evaluated at the mean temperature are taken for each phase compared to a temperature-dependent implementation. An exception is the density. If the density change during melting is not taken into account the deviation of the melt fraction lies between 6 and 8%. In summary, the validation of the numerical model is very satisfactory and demonstrates the suitability of the model for performing the investigations of the part B paper.

Experimentally verified thermodynamic framework for corrosion

Utilizing the foundational principles of thermodynamics, this study characterizes material degradation resulting from corrosion, substantiating the outcomes through experimental verification. The proposed methodology establishes a unified corrosion model, effectively correlating entropy generation with measurable parameters, including potential difference, corrosion current, and temperature. The Degradation Entropy Generation (DEG) theorem is applied to establish a linear relationship between entropy generation and the degradation rate through a constant material property known as the degradation coefficient (B). Material degradation, quantified by assessing the material loss, is systematically examined with a focus on low-carbon steel (LCS 1018) and Al6061-T6. Corrosion experiments were conducted using a three-electrode electrochemical corrosion cell immersed in a 3.5 wt% NaCl aqueous solution. The degradation parameter, B, for both materials was assessed through multiple accelerated corrosion tests, where various magnitudes of potentials were applied to specimens with differing exposed areas. The presented results unveil a consistent degradation coefficient of (30±2)×10−9 m3K/J for LCS 1018 and (25±2)×10−9 m3K/J for Al6061-T6. To ascertain the generalizability of these findings under diverse environmental conditions, additional experiments are conducted on LCS 1018, exposing it to varying environmental parameters such as different percentages of NaCl solution, acidic conditions, and elevated solution temperatures. Remarkably, the degradation coefficient remains constant across all tested corrosive environments, attesting to its independence. This study offers a novel approach to understanding material degradation through a thermodynamic lens and demonstrates the applicability of the proposed corrosion model in diverse and challenging operational conditions.

Influence of concentration-dependent material properties on the fracture and debonding of electrode particles with core–shell structure

Core–shell electrode particle designs offer a route to improved lithium-ion battery performance. However, they are susceptible to mechanical damage such as fracture and debonding, which can significantly reduce their lifetime. Using a coupled finite element model, we explore the impacts of diffusion-induced stresses on the failure mechanisms of an exemplar system with an NMC811 core and an NMC111 shell. In particular, we systematically compare the implications of assuming constant material properties against using Li concentration-dependent diffusion coefficient and partial molar volume. With constant material properties, our results show that smaller cores with thinner shells avoid debonding and fracture regimes. When factoring in a concentration-dependent partial molar volume, the maximum values of tensile hoop stress in the shell are found to be significantly lower than those predicted with constant properties, reducing the likelihood of fracture. Furthermore, with a concentration-dependent diffusion coefficient, significant barriers to full electrode utilisation are observed due to reduced lithium mobility at high states of lithiation. This provides a possible explanation for the reduced accessible capacity observed in experiments. Shell thickness is found to be the dominant factor in precluding structural integrity once the concentration dependency is accounted for. These findings shed new light on the performance and effective design of core–shell electrode particles.

Discontinuous Galerkin method for vibration of structures with piecewise constant material properties

In this work, the vibrations of a structure excited by an impact source are modelled using the time domain nodal discontinuous Galerkin (DG) method, which solves linear elasticity equations. A scaled lightweight wooden floor (LWF) structure which consists of components that differ in their mechanical properties is taken as a case study. The Rankine-Hugoniot jump conditions for piece-wise constant material properties are used to obtain accurate numerical fluxes in the DG method, and their detailed derivation is the main contribution of this work. Free boundary conditions are applied on the surface of the structures, and constant viscous damping force is added to the model to have vibrational energy losses. To validate the numerical results, the mobility of the structure is calculated and compared with experimental data. The agreement is good regarding the natural frequencies, with a maximum absolute difference of less than 11 Hz in the frequency range below 200 Hz. The adopted damping approach is shown to be insufficient to represent a broad frequency range.

Numerical analysis of thermoelectric power generation coupled with temperature-dependent material properties

Thermoelectric generator (TEG) with improved performance is a promising technology in power supply and energy harvesting. Existing studies primarily adopt constant material properties to investigate TEG performance. However, thermoelectric (TE) material properties are subjected to considerable variations with temperature. Thus, reasonable doubts have risen concerning the influence level of temperature-dependent material properties on TEG performance. To solve this problem, an efficient and a comprehensive one-dimensional numerical model is developed to fully consider the third-order polynomial temperature-dependent thermal conductivity, Seebeck coefficient, and electrical resistivity. Control volume and finite difference algorithms are compared, and experiments are conducted to verify the developed numerical model. The temperature distribution along the TE leg obviously differs from the parabolic shape, which is a classic temperature distribution under the assumption of constant material properties. Insights find that the local change rate of thermal conductivity and Thomson effect are the essential reasons for the abovementioned phenomenon. It has been found that Thomson heat is released in the part of the leg near the cold-end, whereas it is absorbed in the remaining parts of the leg near the hot-end. The electric power on the basis of constant material properties is confirmed to be accurate enough by the developed numerical model, but the parabolic shape of the TE efficiency can be only obtained when temperature-dependent material properties are considered. Furthermore, it is wise to improve the TE efficiency by structural optimization. The present work provides an efficient and a comprehensive one-dimensional numerical model to include temperature-dependent material properties. New insights into the temperature and heat flux distribution, Thomson influence, and structural optimization potential are also presented for the in-depth understanding of the TE conversion process.

Enhancing the mechanical stability of restored teeth with interfacial cracks: Finite element analysis

ObjectivesThis study aims to enhance the mechanical stability of restored molar teeth with class II occlusal-distal (OD) cavities. We seek to achieve this goal through a comprehensive investigation of three primary factors: (1) the choice of restoration material properties, (2) internal cavity geometries, and (3) the impact of double-layered restoration configurations. MethodsTo achieve our objectives, we initiated by creating two-dimensional (2D) models of restored teeth featuring class II OD cavities, utilizing scanned and segmented images of maxillary molar teeth. We drew 2D profiles of dentine and enamel, which were then imported into finite element analysis (FEA) software. To explore various cavity geometries, we implemented a total of thirteen different designs, encompassing straight, oblique, grooved, curved, and double-layered configurations. We utilized a semi-circular stone to simulate the application of contact load on the restored tooth. We applied identical boundary conditions and contact loading across all models. To assign material properties, we developed a Python code, enabling the automatic assignment of seven elastic moduli ranging from 2 GPa to 26 GPa to the restoration materials. Meanwhile, constant material properties were assigned to the enamel and dentine. In total, we conducted 133 FEA simulations to comprehensively analyse the effects of the aforementioned factors on the strength and performance of restored molar teeth. ResultsOur analysis revealed two key factors significantly influencing the mechanical resistance of treated teeth, particularly in the presence of a crack or debonding: (1) the marginal geometry of the OD cavity and (2) the elastic modulus of the restorative material. However, altering the internal cavity angle and implementing a double-layered restoration did not significantly influence the restored tooth's overall strength and performance in the face of crack or debonding situations. SignificanceThe findings of this study have substantial implications for designing and restoring class II OD cavities to enhance resistance to cracks or debonding. The use of curved marginal geometries in restoration design can significantly improve fracture resistance, with double-curved geometries reducing stress concentrations by approximately 43% compared to straight cavities. These results offer valuable guidance for strengthening the structural integrity of restored teeth, calling for further experimental investigations to explore practical applications and benefits.

Thermomechanical shakedown analysis considering temperature-dependent yield stress based on the primal-dual eigenstress-driven method

Many industrial structural components are loaded repeatedly in high-temperature environments. The shakedown limit under variable thermomechanical loads is a critical factor in thermomechanical elastoplastic structure design assessment. The shakedown limit is weakened due to material strength reduction at high-temperature conditions.This paper develops an efficient shakedown analysis Primal-dual Eigenstress-driven Method(PEM) algorithm for temperature-dependent yield condition, which overcomes the obstacle of the original PEM method [1] which can only deal with constant material properties. The developed temperature-dependent PEM algorithm proposes a two-level iteration algorithm to determine the shakedown limit and the time-independent residual stress field. At the inner level the theoretical framework tailored to the temperature dependence problem is derived to solve the Karush-Kuhn-Tucker (KKT) conditions of the extended temperature-dependent shakedown theorem and establish an increment algorithm for forming residual stress fields. Besides, the lower bound safe multipliers are computed to verify the residual stress field obtained by inner-level algorithm. At the outer level an efficient fixed-point algorithm is applied to search the shakedown multiplier, where the corresponding updating strategy for the yield stress with temperature is nested. For practicability, the proposed algorithm is seamlessly integrated into commercial platform ANSYS, which is applicable to industrial structures. Four numerical examples from multiple perspectives show the effectiveness of developed PEM method.

Topology optimization of thermo‐elastic structures with temperature‐dependent material properties under large temperature gradient

AbstractIn this work, high temperature and large temperature gradient are addressed for the first time in the topology optimization of thermo‐elastic structures. The conventional assumption of constant material properties (CMPs) is broken through with the full consideration of temperature‐dependent material properties (TDMPs) including thermal conductivity, elastic tensor, and coefficient of thermal expansion. Nonlinear heat conduction is thus implemented to give varying temperature fields in thermoelasticity. The maximum displacement of the specified region is taken as the objective function in the formulation of the optimization problem. The Kreisselmeier‐Steinhauser (KS) function is employed to approximate the regional maximum displacement/temperature. Corresponding sensitivity analyses, which are carried out using the adjoint method, theoretically reveal how TDMPs affect the thermo‐elastic optimization problem. Typical numerical examples are investigated to validate the proposed approach. The results show that the use of TDMPs produces optimized structures of high fidelity with displacements precisely predicted and temperature constraints rigorously satisfied under large temperature gradient, while thermo‐elastic analysis and optimization with CMPs lead to undesirable designs with significant inaccuracy.

Parametric study of 1D plasma photonic crystals with smooth and discontinuous density profiles

Plasma photonic crystals (PPCs) have the potential to significantly expand the capabilities of current millimeter wave technologies by providing high speed (microsecond time scale) control of energy transmission characteristics in the GHz through low THz range. Furthermore, plasma-based devices can be used in higher power applications than their solid-state counterparts without experiencing significant changes in function or incurring damage. Plasmas with periodic variations in density can be created externally, or result naturally from instabilities or self-organization. Due to plasma's diffuse nature, PPCs cannot support rapid changes in density. Despite this fact, most theoretical work in PPCs is based on solid-state photonic crystal methods and assumes constant material properties with abrupt changes at material interfaces. In this work, a linear model is derived for a one-dimensional cold-plasma photonic crystal with an arbitrary density profile. The model is validated against a discontinuous Galerkin method numerical solution of the same device configuration. Bandgap maps are then created from derived group velocity data to elucidate the operating regime of a theoretical PPC device. The bandgap maps are compared for one-dimensional PPCs with both smooth and discontinuous density profiles. This study finds that bandgap behavior is strongly correlated with the density profile Fourier content and that density profile shapes can be engineered to produce specific transmission characteristics.

Modeling of FGM contacts using piecewise linear variation in Young’s modulus

Functionally graded materials (FGM) are used as coatings at contact interfaces to tailor the desired surface properties while avoiding sudden changes in material properties. This work investigates the full-sliding frictional contact between a rigid indenter and FGM-coated half-space under plane-strain conditions. The FGM-coating is divided into a number of sublayers, with Young’s modulus varying linearly in each sublayer, effectively making the overall variation piece-wise linear. This approach overcomes the disadvantage of discontinuity of material properties at the interfaces of sublayers that exists in multi-layered piecewise constant modeling. Series solution approach based on the solution to the singular integral equation that characterizes the 2D contact is considered. In this approach, pressure distribution at the interface is expressed as a series expansion. This approach can be used to analyze any arbitrarily shaped contacts. The results show that the piecewise linear FGM modeling approach with tractions expressed as modified Fourier series is a more accurate and efficient way of representing FGM material property as compared to piecewise constant material properties, which are used in most of the existing literature. The number of layers needed to converge in continuous variation is also very less compared to the piece-wise constant and hence the computational time is less.

Large Component Simulation of an Inboard Sector of a Dual-Coolant Lead-Lithium Blanket

Advances in high-performance computing now enable the engineering evaluation of large blanket components from a systems perspective at the beginning of a normal design cycle. As an example, we discuss the computational fluid dynamics (CFD) involved in characterizing the thermal performance of an entire 22.5 toroidal sector of a dual-coolant lead-lithium blanket with particular attention to the integrated manifolding and flow distributions. The inboard sector is roughly 7 m tall, has 321 first-wall helium-cooled channels, and five parallel PbLi breeder channels complete with insulating SiC flow channel inserts. A finite volume model was developed with various degrees of mesh refinement from 36 to 187 million cells to perform the flow calculations on disparate fluids with conjugate heat transfer in the solid. Steady-state CFD calculations were performed using a realizable k-ε turbulence model. Simplifications include a uniform applied surface heat flux and a one-dimensional radial volumetric neutron heating profile. Constant material properties were used for the F82H reduced-activation ferritic martensitic (RAFM) steel walls, SiC flow channel inserts, and the PbLi breeder. Ideal gas behavior was assumed for the helium, which includes compressibility. Helium mass flows of 54 kg/s at 8 MPa and PbLi flows of 3 kg/s at 101 kPa supply the sector, both at an inlet temperature of 350°C. This early model is not optimized; however, it reveals important features not obvious in a conglomeration of smaller independent models. For example, all the manifolding was included to evaluate flow distributions throughout the full component. Submodels were only used to obtain the convective heat transfer coefficients (HTCs) inside the helium first-wall channels equipped with enhancement vanes that allow the first wall to handle 0.8 MW/m2 of plasma heat flux with the aim of keeping bulk RAFM steel temperatures near the creep-fatigue limit of 550°C. Average HTCs obtained from these detailed submodels were then used in the large model to predict thermal performance without incurring the meshing overhead from the thousands of internal vanes. Although much progress was made, initial results indicate that more must be done to further reduce hot spots on the first wall, minimize pressure drops, and provide optimal flow distributions.

Axial Compression Study of Crash Boxes with Various Honeycomb Structures

In recent times, automotive manufacturing companies are focusing on developing components that is capable of increasing safety features associated with lightweight materials such as using aluminium. One such innovation is providing the vehicle with crash box, which is generally located at the front bumper. The function of the crash box is to safeguard the passenger by absorbing the kinetic energy of collision and self-deformation. In this paper, the authors presented a study of the compressive test applied on crash boxes with different types of honeycomb sandwich circular columns using 3D virtual modelling and finite element (FE) simulation with the help of Solidworks and Ansys Workbench respectively. This sandwich structure comprises two circular aluminium tubes filled with core shaped as a large-cell honeycomb lattice. Here, the crash boxes with three different honeycomb sandwich circular columns i.e., hexagonal, triangular, and semi-circular arrangement, were investigated and the energy absorption capabilities of these columns were studied. FE simulations were used to evaluate maximum stress that a material can sustain over a period under a load, material deformation, geometric changes, and load-displacement results using a constant material property of that of aluminium alloy, and the results of the three different arrangements were compared and it is known that the crash box with semi-circular arrangement has high energy absorbing capacity.

Active responses of nanoparticle-polymer interface/interphase via the interfacial interaction redistribution

Physical responses of nanoparticle (NP)-polymer interphase/interface to external stimulus are a topic of great interest in nanocomposites. Previously, the interphase was tacitly assumed to have passive responses with constant material properties during deformation while the interface was mainly studied under hydrostatic loadings. To explore the unique features of the interphase we used a full-atom molecular dynamics simulation to monitor the evolution of its mass density and atomic stress profiles during deformation. A cohesive zone model was then used to define the key parameters for the NP-polymer interaction, which enable one to study the responses of the interface without spherical symmetry and understand the unique behavior of the stretched interphase/interface. The conceptual change has been achieved showing that an external strain can redistribute the NP-polymer interaction to affect the high compression in the interphase, the physical origin of the interface confinement effect in the nanocomposite. This eventually triggers the active responses of the interphase leading to the apparent strain-dependence of the mass density and some other properties. The redistribution of the interfacial interaction also brings about the stable, metastable and unstable status of the stretched interface characterized by the strain-dependent modulus and interface debonding.

The Gap test – Effects of crack parallel compression on fracture in carbon fiber composites

This paper explores the global Mode I fracture energy of a carbon fiber composite subject to a biaxial stress state at the crack tip, specifically in which one stress component is compressive and parallel to the crack. Based on an experimental technique previously coined as The Gap Test and Bažant’s Type II Size Effect Law, it is found that there is a monotonic decrease in the Mode I fracture energy as the crack parallel compressive stress increases. Compared to the nominal value of fracture energy, where no crack parallel compression is applied, the fracture energy is observed to decrease by up to 37% for a compressive stress equal to 44% of the compressive failure limit of the composite. This weakening effect is attributed to splitting cracks that are induced at the crack tip due to the crack parallel compression, which are identified via crack tip photomicroscopy. This is a novel result that challenges the century old hypothesis of fracture energy being a constant material property and further, shows for the first time that crack parallel compression leads to a composite structure being dangerously weaker than expected.The experimental campaign is also buttressed with a computational campaign that provides a framework capable of capturing the effects of crack parallel compression. Through the use of the crack band model, which correctly characterizes the fracture process zone tensorially, coupled with a fully tensorial damage law, the simulated results provide satisfactory agreement with the experimental data. Conversely, when a reduced tensorial damage law defines the crack band it is shown that the structural strength and fracture energy are dangerously overpredicted. This emphasizes the importance of using a crack band model coupled with a fully tensorial damage law to accurately predict fracture in composites.

Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems

Abstract We introduce and analyse various regularized combined field integral equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically starting from suitable coercive approximations of Dirichlet-to-Neumann operators (DtN), and we present a periodic pseudodifferential calculus framework within which the well posedness of CIER formulations can be established. We also use the DtN approximations to derive and analyse OS methods for the solution of elastodynamics transmission problems. The pseudodifferential calculus we develop in this paper relies on careful singularity splittings of the kernels of Navier boundary integral operators, which is also the basis of high-order Nyström quadratures for their discretizations. Based on these high-order discretizations we investigate the rate of convergence of iterative solvers applied to CFIER and OS formulations of scattering and transmission problems. We present a variety of numerical results that illustrate that the CFIER methodology leads to important computational savings over the classical CFIE one, whenever iterative solvers are used for the solution of the ensuing discretized boundary integral equations. Finally, we show that the OS methods are competitive in the high-frequency high-contrast regime.

Orthodontic shear bond strength and ultimate load tests of CAD/CAM produced artificial teeth

ObjectivesTo investigate whether artificial CAD/CAM processed (computer-aided design/manufacturing) teeth could be a feasible option for the production of dental in vitro models for biomechanical testing.Material and methodsDisks (n = 10 per group) made from two different CAD/CAM-materials, one fiber-reinforced composite (FRC; Trinia, Bicon) and one polymethylmethacrylate-based resin (PMMA; Telio CAD, Ivoclar Vivadent), as well as bovine teeth (n = 10), were tested for their shear bond strength (SBS) and scored according to the adhesive remnant index (ARI). In addition, CAD/CAM-manufactured lower incisor teeth were tested for their ultimate load (Fu).ResultsWith regard to SBS, both PMMA (17.4 ± 2.2 MPa) and FRC (18.0 ± 2.4 MPa) disks showed no significant difference (p = 0.968) compared to bovine disks (18.0 ± 5.4 MPa). However, the samples differed with regard to their failure mode (PMMA: ARI 4, delamination failure; FRC: ARI 0 and bovine: ARI 1.6, both adhesive failure). With regard to Fu, FRC-based teeth could withstand significantly higher loads (708 ± 126 N) than PMMA-based teeth (345 ± 109 N) (p < 0.01).ConclusionUnlike PMMA-based teeth, teeth made from FRC showed sufficiently high fracture resistance and comparable SBS. Thus, FRC teeth could be a promising alternative for the production of dental in vitro models for orthodontic testing.Clinical relevanceCAD/CAM-processed teeth made from FRC enable the use of standardized geometry and constant material properties. Using FRC teeth in dental in vitro studies has therefore the potential to identify differences between various treatment options with rather small sample sizes, while remaining close to the clinical situation.

Cyclic heat engines with nonisentropic adiabats and generalization to steady-state devices including thermoelectric converters.

For heat engines (including refrigerators) the separation of total entropy production in reversible parts ΔS and irreversible contributions has proved to be very useful. The ΔS are entropies for ideal lossless processes at the hot- and cold side and are important system parameters. For Carnot-like heat engines performing finite-time cycles, the concern was raised in a preceding paper that the ΔS are not always independent from irreversibilities, if initial and final working fluid temperatures T_{f}(t) differ in the isothermal transitions. It turns out that the ΔS are unchanged and independent, if T_{f} (t) evolution is optimized for entropy minimization and apparent inconsistencies are cleared up. If nonisentropic transitions in the adiabatic cycle branches are taken into account, the difference of cold- and hot-side entropy reversibilities is equal to the entropy production in the adiabats. Maximization of cooling power is studied for various irreversible entropy models. The concepts are extended to noncyclic steady-state engines. Power maximization and efficiency calculations are performed exactly analytically. This serves as prerequisite for the hitherto unsolved problem of an accurate definition of reversible and irreversible entropy parts in thermoelectric (TE) converters in the case of inhomogeneous three-dimensional material distributions. It is revealed that for nonconstant Seebeck coefficients, additional terms to the Joule heat arise that destroy positive generator performance in the limit of heat conductance k→0, in contrast to the traditional constant material properties model. Thus, the concept of improving TE materials by reducing k is in question and an adapted figure of merit Z is presented to deal with the situation.

The influence of dental restoration depth, internal cavity angle, and material properties on biomechanical resistance of a treated molar tooth

ObjectivesTo assess the hypotheses that a restored tooth structure for a class II occlusal-distal (OD) cavity can be reinforced by optimizing the cavity geometry and choosing composites with adequate mechanical properties. MethodsA human maxillary molar tooth was scanned, and segmented. The 2D profiles of dentin and enamel were drawn and imported to ABAQUS software. Eighteen restored tooth models with different cavity occlusal depths (OcDs) and internal cavity angles were developed. A semi-circular stone part was used to apply contact loads to the restored tooth model. After setting up the required interactions and boundary conditions, a written Python code was used to automatically assign a wide range of elastic moduli, from 2 GPa to 26 GPa, to the composite restorations, and assign constant material properties to the enamel and dentine.For simplicity, the behaviour of the mechanical material was postulated homogeneous and elastic, while the FE analyses were linearly carried out in this study. Also, the code enabled the FEA software to conduct the stress analyses, determine maximum principal stresses, and record the obtained results. ResultsThe internal cavity angle formed between the mesial wall and the pulpal floor of the cavity significantly changed the peak maximum principal stress both in the enamel and restoration. The peak stress concentrations were observed mostly at the enamel-restoration interface, with an almost perpendicular orientation to this interface. Regarding the effect of occlusal cavity depth (OcD), the model with the shallowest cavity (OcD = 1.5 mm) represented greater resistance to applied loads than the model with deeper cavities (OcD = 2.0 mm and OcD 2.5 mm). The composite modulus (CM) in the range of 10–18 GPa reduced the maximum principal stress concentrations in the enamel. The lowest result for maximum principal stress was observed in the model with OcD = 1.5 mm, CM = 10 GPa and internal cavity angles = 100°, which was the strongest model against contact loads. SignificanceClass II OD cavities with optimal geometry have reduced induced stress levels, thus being able to be more mechanically robust against contact load transmitted by a stone. Cavity geometry designs with obtuse (more than 90°) internal cavity angles were significantly efficient in minimizing peak stress concentrations. The results indicated that for the model with obtuse internal cavity angles, choosing a composite with optimised properties can diminish stress, particularly at the tooth-restoration interface. Furthermore, the shallowest the cavity, the sturdier the restoration was, especially when the interface tooth-restoration laid on enamel and not on dentine.

Disrupt the upper or the lower conduit? The dual role of gas exsolution in the conduits of persistently active volcanoes

Many volcanoes emit a significant portion of the gas they transport to the atmosphere during continual passive degassing rather than during eruptions. To maintain a high gas and thermal flux without erupting magma, the flow field in the volcanic conduit must be approximately balanced with gas-rich, buoyant magma ascending and degassed, heavy magma descending. In vertical conduits, this exchange flow takes the form of core–annular flow, where the gas-rich magma forms a core enclosed by an annulus of degassed magma. The flow dynamics of core–annular flow have been studied extensively in fluid dynamics, but mostly for constant material properties. Our study aims to advance our understanding of how core–annular flow responds to volatile exsolution – a simple, yet ubiquitous disruption in volcanic conduits, which alters both the density and the viscosity of the core fluid. By deriving an evolution equation for the core–annular interface based on a generalized exchange-flow condition using a lubrication approximation, we find that the response of the system to volatile exsolution depends on the conduit flow regime. The same nucleation event can lead to a flow adjustment only in the upper, only in the lower or in both portions of the volcanic conduit. Our results emphasize that the thermodynamic evolution of magma properties and volcanic conduit flow are intricately linked, which may help understand the observed variability of eruptive behaviour at persistently degassing volcanoes.